Aleksandar Tasic - TU Delft OCW · [email protected] © 2006 Job Advertisement • RF/analog...

[email protected] © 2006

Oscillators Oscillators Aleksandar Tasic

Electronics Research Laboratory

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Job AdvertisementJob Advertisement

• RF/analog circuits design experience• LNA, mixer, VCO, PLL, filter, A/D, PA

• CAD proficiency• Cadence, ADS, Spice

• Packaging, measurement, and PCB design skills are strongly encouraged

• Programming in C is an asset

• Salary experience based, 80.000 – 120.000

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UMTS VCO RequirementsUMTS VCO Requirements

VCO design parameters Design requirement Oscillating frequency 2.1GHz

Tuning range 400MHz Voltage swing 0.7V Phase noise -110dBc@1MHz

Supply voltage 3V Power consumption 10mW

Technology parameters Values Technology BiCMOS

Number of metals 4 Transit frequency 50GHz MIM capacitors available

Varactors available

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OutlineOutline

• Oscillator Classification, Oscillation Condition and Frequency

• LC Oscillators• Oscillation Signal Steady-State Amplitude• Interpretation of Noise in Oscillators• Linear Phase-Noise Model• Spectral Analysis of Phase Noise • Design Procedure for LC-Oscillator • Simulations/Layout/Measurements

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Oscillator DefinitionOscillator Definition

• An oscillator is a tunable circuit that generates a stable periodical signal, which is in the limit independent of the initial conditions.

• A non-linear system that should be of a second order (with two time constants).

0)()())(()( 22

2

=++ txtxdtdtxftx

dtd ω

non-linear functionoscillation signal angular frequency

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Oscillator Classification Oscillator Classification ––Time Time Constants BasedConstants Based

frequency dominated by oscillator order

1 time constant 1st-order oscillator

2 time constants 2nd-order oscillator

… …

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Oscillator Classification Oscillator Classification ––Resonator BasedResonator Based

• Resonator oscillators• LC oscillators, negative resistance oscillators

• good phase noise properties• poor quadrature accuracy

• Resonatorless oscillators• Ring oscillators

• poor phase noise properties• good quadrature accuracy

• Relaxation oscillators• poor phase noise properties• good quadrature accuracy

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Oscillator Positive Feedback Oscillator Positive Feedback ModelModel

ForwardNetwork

G(s)

FeedbackNetwork

H0(s)

+X Y

)s(H)s(G)s(G

)s(X)s(Y)s(H

01−==

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Oscillation ConditionOscillation Condition

• Barkhausen’s criteria• Loop-gain module > 1 (start up)

• Loop-gain module equals 1 (steady state)

• Phase shift around the loop equals 360º( )( ) πω 2=∠ jT

( ) ( ) ( ) 10 =⋅= ωωω jHjGjT

( ) ( ) ( ) 10 >⋅= ωωω jHjGjT

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Resona tor

Resona tor

ALC

y(x) y(x)

Integrator

Schmitt trigger

Nonlinear amplifier

• 2nd-order oscillator• 2nd-order timing constant• amplitude limiter

• 1st-order oscillator• 1st-order timing constant• Schmitt trigger

Oscillator ModelsOscillator Models

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LC VCO

LC VCO

1st–order oscillatorinjection-lock ring oscillator

RC ring oscillatorLC oscillator

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Oscillator ApplicationOscillator Application

• Frequency conversion• Downconversion in receivers• Upconversion in transmitters

• Clock generation• Channel selection• Modulation/demodulation

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LC Oscillators LC Oscillators

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Generalized LC Oscillator CircuitGeneralized LC Oscillator Circuit

• Loop-gain approach: T(jω)=1

• Impedance matrix approach: det(Z)=0 (or det(Y)=0)( ) ( ) ( )1 3 1 1 21 0IN IN MZ Z Z Z Z Z g Z+ + + + =

• Single transistor model

Z1

Z2

ZLZ3

Z , gMIN M

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Examples of LC OscillatorExamples of LC Oscillator

Colpitts

Hartley

Clapp

)CC/(CLC 21210

1+

=ω

0

21 2(1 ) mn C C r gω− <

, r, r

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Negative Resistance OscillatorNegative Resistance Oscillator

C CL,

UT

V CC

RLV V

Q1 Q2

ITAIL

QCSQCS

resonating LC tank

active pair

biasing current source

Mg−

2/1

0VLC

=ω

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Negative Resistance Oscillator Negative Resistance Oscillator -- Simplified ModelSimplified Model

LC/10==ωω

TKM Gg >• oscillation condition

2/mM gg =

• oscillation frequency2/CC V=

GTK C L-gM

+V-

gMV

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202

0

)(2)(

CRL

RG CL

TK ωω

+=

• tank conductance

0

0

1 L CL V C

LQ QR C Rω

ω= =

• quality factors

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

CLTK QQL

G 111

0ω

C

2R C

L

RL

GTK C L

LC TankLC Tank

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© 2005, A. Tasic 19

Resonator Impulse ResponseResonator Impulse Response

LC/L/sRsLC)s(I)s(I)s(H

LS

L

111

2 ++==

tsn

i i

i

S

LL

ie)'s(Q)s(P

)s(I)s(I)t(i ∑

=

−

=

=

0

1

tsin)/(

e)t(i

t

L ωωσ

ω σ

20

0

1−=

LC/10=ω

L/RL 2−=σ

σ

ω

200 1 )/( ωσωω −=

resonator pole patternωσ jsi ±=

δ R SC

Lis(t)iL(t)

L

[email protected] © 2006 19


ω0

σ

ω

LCCgCGsss

CsH

MTK /1)//(1)( 2 +−+

=

)(1)()(

sZgsZsH

M−=

LC/10==ωωTKM Gg >

Oscillator System Transfer FunctionOscillator System Transfer Function

system pole pattern

• oscillation condition and frequency

GTK C L-gM

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SteadySteady--State State Oscillation Signal Oscillation Signal

Amplitude Amplitude

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SubSub--OutlineOutline

• Differential Pair Characteristic• Large-Signal Conductance• Steady-State Oscillation Signal Amplitude

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Amplitude StabilizationAmplitude Stabilization

• Amplitude regulator• amplitude control mechanism

Resonator

Resonator

ALC

y(x) y(x)

• Nonlinear amplifier• well defined nonlinearity

• timing reference loss compensation

• loop-gain control

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IOUT

VIN

1/f0

1/f0

Differential CharacteristicDifferential Characteristic

⎟⎠⎞

⎜⎝⎛= tcosxtanhI)t(iOUT ω

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I0

-I0

tcosV)t(vIN ω1=

TT VV V/Vx >>= 11

( )∑ −=+++= −n

nOUT tncosaI...tcosItcosItcosI)t(i ωωωω 1253 120531

)x(aI)x(I nn 0=

• current harmonic content

∫− ⎟⎠⎞

⎜⎝⎛=

π

πθθθ

πd)ncos(cosxtanh)x(an 2

1

Q1 Q2

I OUT

VIN

I 02

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Large Signal (Trans)ConductanceLarge Signal (Trans)Conductance

II

VV

VI

VIxG T

TM

0

1

1

0

1

11 )( ==

xxag

II

xgxG MmM

)(21)( 1

0

11 ==

xxagxG MM)(2/)( 1

1 =

GM1(x)/gM

x

1

0.5

1 10

( ) ( )

gain loop signal small1

uctance)trans(cond signal smallductance(trans)con lfundamenta signal large

=

=⋅ 1011 ωjHg

gVG

MM

M

• steady state oscillation condition ( ) ( ) 1011 =⋅ ωjHVGM

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Large Signal ComponentsLarge Signal Components

( )∑∞

=− −=+++=

0120531 12cos...5cos3coscos)(

nnOUT tnaItItItIti ωωωω

• output current

• close to square wave if V1 >> VT

nI

nI

I TAILn ππ

24 0 ==

• harmonics of the square-wave signal current

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11

1

1

111

2)(V

I V

I I

IVIVG TAILTAIL

TAILM π

===kg

VG

M

M 1)( 11 =

lfundamenta current resistance tanklfundamenta voltage ×=

= TKTAIL RI Vπ2

1

• steady state fundamental amplitude

• small signal loop gain (k)

MTK gRk =

• large signal conductance and steady state oscillation condition

Steady State Signal AmplitudeSteady State Signal Amplitude

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So FarSo Far

VCO design parameters Design requirement Oscillating frequency 2.1GHz

Tuning range 400MHz Voltage swing 0.7V Phase noise -110dBc@1MHz

Supply voltage 3V Power consumption 10mW

Technology parameters Values Technology BiCMOS

Number of metals 4 Transit frequency 50GHz MIM capacitors available

Varactors available

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Interpretation of Interpretation of Noise in Noise in

OscillatorsOscillators

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SubSub--OutlineOutline

• Signal Phasor Description• Signal Spectral Description• Phase-Noise Definition• Phase-Noise Specification

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Bennett Noise InterpretationBennett Noise Interpretation

( )kkk tatn θω += cos)(

• White noise spectrum (power spectral density)

• One noise component (time domain)AfN =)(

• ak – known amplitude

• ωk – known angular frequency

• θk – random phase (constant and uniform)

)2( A=

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Oscillation Signal DescriptionOscillation Signal Description

• Ideal vs. actual oscillation signalV0cosω0t vs. V0[1+a(t)]cos[ω0t+θ(t)]• a(t) amplitude modulated component

• θ(t) phase modulated component

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Oscillation Signal Oscillation Signal PhasorPhasorDescriptionDescription

• in-phase component (AM) can be removed

• quadrature-phase component (PM) is unavoidable

)(ta

)(tθ

a(t)

n(t)

v(t)

)(tθ

( ) ( ) ( ) ( )ttttattttatv tn 0000)( sin)(cos)(cos)(cos)](1[)( ωθωωθω −+≈++=+

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Oscillation Signal Oscillation Signal PhasorPhasorDescriptionDescription

a(t)

n(t)

v(t)

)(tθ

( ) ( ) ( ) ( )ttttattttatv tn 0000)( sin)(cos)(cos)(cos)](1[)( ωθωωθω −+≈++=+

• amplitude control mechanism

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Oscillation Signal Spectral Oscillation Signal Spectral DescriptionDescription

=

+

AM

PM

f0 Δf+f0

• oscillating signal and noise component

• amplitude modulated component

• phase modulated component

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• oscillating signal and noise component

• amplitude control mechanism

• phase modulated component

Oscillation Signal Spectral Oscillation Signal Spectral DescriptionDescription

=

+

AM

PM

f0 Δf+f0

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Phase Spectrum vs. Oscillation Phase Spectrum vs. Oscillation Signal SpectrumSignal Spectrum

)()()()()( 0000 fffffffffV +Θ+−Θ+++−≈ δδ

0

f0-f0

( )fΘ• phase spectrum

• oscillation signal spectrum

( ) ( )( )( ) ( ) ( )ttAtA

ttAttAtv

kkk

kkk

00

00

sinsincossincos)(cos)(ωφωθω

φωθωθω+−≈

≈++=+=

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Phase Noise DefinitionPhase Noise Definition

• ratio of the noise power in a 1Hz bandwidth at frequency f0+Δf and the carrier power

(Δω)=10log[Pside-band(ω0+ Δω)/Pcarrier (ω0)] [dBc/Hz]

L

L

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Why is Phase Noise Important?Why is Phase Noise Important?

• Reciprocal mixing• desired signal covered by the

phase-noise skirt of the interferer

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Phase Noise SpecificationPhase Noise Specification

• Typical blocking profile

• Specra of downconverted signals

BW

blocker

S/N

desired signal (MDS)

Δf

(Δf)=SMDS-SBLOCK-10logBW-S/N [dBc/Hz]

S/N=SMDS-NxBW

=N/SBLOCKL

L40

Aleksandar Tasic - TU Delft OCW · [email protected] © 2006 Job Advertisement • RF/analog...

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Transcript of Aleksandar Tasic - TU Delft OCW · [email protected] © 2006 Job Advertisement • RF/analog...